Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
| dc.creator | Batyrev, Victor V. | |
| dc.date | 1993-10-05 | |
| dc.date.accessioned | 2026-07-07T09:05:55Z | |
| dc.date.available | 2026-07-07T09:05:55Z | |
| dc.description | We consider families ${\cal F}(Δ)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $Δ$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials $f$ with a fixed $n$-dimensional Newton polyhedron $Δ$ in $n$-dimensional algebraic torus ${\bf T} =({\bf C}^*)^n$. If the family ${\cal F}(Δ)$ defined by a Newton polyhedron $Δ$ consists of $(n-1)$-dimensional Calabi-Yau varieties, then the dual, or polar, polyhedron $Δ^*$ in the dual space defines another family ${\cal F}(Δ^*)$ of Calabi-Yau varieties, so that we obtain the remarkable duality between two {\em different families} of Calabi-Yau varieties. It is shown that the properties of this duality coincide with the properties of {\em Mirror Symmetry} discovered by physicists for Calabi-Yau $3$-folds. Our method allows to construct many new examples of Calabi-Yau $3$-folds and new candidats for their mirrors which were previously unknown for physicists. We conjecture that there exists an isomorphism between two conformal field theories corresponding to Calabi-Yau varieties from two families ${\cal F}(Δ)$ and ${\cal F}(Δ^*)$. | |
| dc.description | 43 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9310003 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9310003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149841 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties | |
| dc.type | text |